Finite Group Databasebeta

← #11795353

Subgroups — #11795353

Order 1152.

294 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593755C211yesmaximal, characteristic
2#10593387C211yesmaximal, characteristic
3#10590584C211yesmaximal, characteristic
4#10590582C211yesmaximal, characteristic
5#10590052C211yesmaximal, characteristic
6#10590052C211yesmaximal, characteristic
7#10590051C211yesmaximal, characteristic
8C2×#3788C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10#64101C2211yescharacteristic
11#63900C2211yescharacteristic
12#63900C2211yescharacteristic
13C2×#3712C2211yescharacteristic
14C2×#3712C2211yescharacteristic
15#63779—21no—
16C4⋊#622—21no—
17#63742—21no—
18#63742—21no—
19C3×#808—21no—
20C3×#807—21no—
21#63575—21no—
22#63573—21no—
23#4881—61no—
24#4861—61no—
25C2×C4×C3⋊D3C2311yescharacteristic
26C2×#624—21no—
27C2×#624—21no—
28C2×#622—21no—
29C2×#622D411yescharacteristic
30C2×#622D411yescharacteristic
31#3788—21no—
32#3788—21no—
33#3787—21no—
34#3787—21no—
35C32×C4⋊C4D411yescharacteristic
36#3752—21no—
37C4⋊(C3⋊Dic3)D411yescharacteristic
38C4×C3⋊Dic3—21no—
39C3×C4⋊Dic3—21no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—21no—
42C2×C3×C3⋊C8—21no—
43#3724—21no—
44#3724—21no—
45#3712—21no—
46#3712—21no—
47#3712Q812yes—
48#3712Q812yes—
49#2090—91nomaximal, Sylow
50C2×ΓL(1,𝔽25)—61no—
51C2×ΓL(1,𝔽25)—61no—
52#892—61no—
53#892—61no—
54D3×C4⋊C4—61no—
55D3×C4⋊C4—61no—
56C3×#107—61no—
57C3×#106—61no—
58#818—61no—
59#817—61no—
60#808—21no—
61#808—61no—
62#807—21no—
63#807—61no—
64C22×C3⋊D3#4111yescharacteristic
65C2×C32×C4—21no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3C2×Q811yescharacteristic
70C4×C3⋊D3C2×Q811yescharacteristic
71C4×C3⋊D3#4111yescharacteristic
72C4×C3⋊D3#4111yescharacteristic
73C2×C3×Dic3—41no—
74C2×C3×Dic3—41no—
75#624—81no—
76#624—81no—
77#622—21no—
78#622—21no—
79#622—41no—
80C3×C3⋊C8—22no—
81C3×C3⋊C8—22no—
82#428—91no—
83#428—91no—
84C2×#106—91no—
85#424—91no—
86#343—91no—
87#343—91no—
88#341—91no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—121no—
92C2×C4×D3—121no—
93C2×C3×C8—61no—
94C2×C3×C8—61no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—61no—
98C3×C4⋊C4—61no—
99(C2×D3)⋊C4—121no—
100(C2×D3)⋊C4—121no—
101C4⋊Dic3—21no—
102C4⋊Dic3—21no—
103C4⋊Dic3—61no—
104C4⋊Dic3—61no—
105Dic3⋊C4—121no—
106Dic3⋊C4—121no—
107C4×Dic3—121no—
108C4×Dic3—121no—
109C2×C3⋊C8—21no—
110C2×C3⋊C8—21no—
111ΓL(1,𝔽25)—62no—
112ΓL(1,𝔽25)—62no—
113ΓL(1,𝔽25)—62no—
114ΓL(1,𝔽25)—62no—
115C22×C32#12111yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3#12511yescharacteristic
119C2×C3⋊D3#12511yescharacteristic
120C32×C4—41no—
121C32×C4C22⋊Q811yescharacteristic
122C32×C4C22⋊Q811yescharacteristic
123C3⋊Dic3—41no—
124C3⋊Dic3#12311yescharacteristic
125C3⋊Dic3C4⋊Q811yescharacteristic
126C3×Dic3—81no—
127C3×Dic3—81no—
128C2×M16—91no—
129C2×M16—91no—
130C2×M16—91no—
131C22×C8—91no—
132#117—91no—
133C2×C4⋊C4—91no—
134C2×C4⋊C4—91no—
135#107—61no—
136#107—181no—
137#106—61no—
138#106—181no—
139#106—181no—
140#106—181no—
141C4⋊C8—181no—
142C4⋊C8—181no—
143C22×D3—61no—
144C22×D3—61no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—41no—
148C2×C3×C4—41no—
149C2×C3×C4—121no—
150C2×C3×C4—121no—
151C2×Dic3—41no—
152C2×Dic3—41no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C4×D3—61no—
158C4×D3—61no—
159C4×D3—61no—
160C4×D3—61no—
161C4×D3—61no—
162C4×D3—61no—
163C4×D3—61no—
164C4×D3—61no—
165C4×D3—242no—
166C4×D3—242no—
167C3×C8—62no—
168C3×C8—62no—
169C3⋊C8—22no—
170C3⋊C8—22no—
171C2×C32#39811yescharacteristic
172C2×C32#47111yescharacteristic
173C2×C32#47111yescharacteristic
174C3⋊D3—21no—
175C3⋊D3—21no—
176C22×C4—91no—
177C22×C4—181no—
178C22×C4—181no—
179M16—92no—
180M16—92no—
181M16—181no—
182M16—181no—
183M16—181no—
184M16—181no—
185C2×C8—61no—
186C2×C8—61no—
187C2×C8—91no—
188C2×C8—91no—
189C2×C8—181no—
190C2×C8—181no—
191C2×C8—181no—
192C4⋊C4—61no—
193C4⋊C4—61no—
194C4⋊C4—91no—
195C4⋊C4—181no—
196C4⋊C4—181no—
197C4⋊C4GO+(4,𝔽2)11yescharacteristic
198C22⋊C4—181no—
199C42—181no—
200C22×C3—21no—
201C22×C3—21no—
202C2×D3—61no—
203C2×D3—61no—
204C2×D3—61no—
205C2×D3—61no—
206C2×D3—121no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—121no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—81no—
215C3×C4—81no—
216C3×C4—241no—
217C3×C4—241no—
218Dic3—61no—
219Dic3—61no—
220Dic3—61no—
221Dic3—61no—
222Dic3—81no—
223Dic3—81no—
224Dic3—241no—
225Dic3—241no—
226C32#209011yescharacteristic, complemented, Sylow
227C23—91no—
228C2×C4—21no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—91no—
234C2×C4—121no—
235C2×C4—121no—
236C2×C4—181no—
237C2×C4—721no—
238C2×C4—721no—
239C2×C4C2×GO+(4,𝔽2)11yescharacteristic
240C8—62no—
241C8—62no—
242C8—181no—
243C8—181no—
244C8—361no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251D3—121no—
252D3—121no—
253D3—121no—
254D3—121no—
255C22—91no—
256C22—91no—
257C22—181no—
258C22—181no—
259C22#6424211yescharacteristic
260C4—41no—
261C4—91no—
262C4—91no—
263C4—241no—
264C4—241no—
265C4—361no—
266C4D32⋊Q811yescharacteristic
267C4D32⋊Q811yescharacteristic
268C3—21no—
269C3—21no—
270C2—181no—
271C2—181no—
272C2#1059334011yescharacteristic
273C2#1059346711yescharacteristic
274C2#1059348111yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3#41
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2090
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
226. C32#2090semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105937552
#105933872
#105905842
#105905822
#105900522
#105900512
#20909